Whenever a car pitstops, why is it that the other team's mechanics has to pull some wire for them? Any clue?

Air hoses. Though in most cases, it's not even needed but they do it out of courtesy.

Well, that and they don't want a major accident happening in the pit lane and their equipment being damaged. It's not needed in IndyCar as their stops are slower due to many factors such as refuelling and not having a dedicated crew for each wheel, but they also have the air guns just on loose pipes they throw to one side when done with.

_________________"We can not drive slower, just to make the races more exciting." Alain Prost

I was expecting that video as it is a great example of what can go wrong. Surprised this doesn't happen more often, though I suppose it is easily avoided, but given the nature of short notice pit stops in F1 you might expect to see it sometimes (team A waits in garage until car A is almost ready to come in then runs out, team B might not have time to respond).